Nuclear installation on river unstable at core (7)
I believe the answer is:
reactor
'nuclear installation' is the definition.
(I've seen this before)
'river unstable at core' is the wordplay.
'river' becomes 'r' (abbreviation for river).
'unstable' is an anagram indicator.
'at'+'core'='atcore'
'atcore' with letters rearranged gives 'eactor'.
'r'+'eactor'='REACTOR'
'on' is the link.
(Other definitions for reactor that I've seen before include "(Nuclear) powerplant" , "power supplier" , "Device to produce energy by nuclear fission" , "Producer of nuclear energy" , "I swing back" .)